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<div class="title">Eigen::JacobiRotation&lt; Scalar &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseMatrixManipulation__chapter.html">Dense matrix and array manipulation</a> &raquo; <a class="el" href="group__DenseMatrixManipulation__Reference.html">Reference</a> &raquo; <a class="el" href="group__Jacobi__Module.html">Jacobi module</a></div></div>  </div>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename Scalar&gt;<br />
class Eigen::JacobiRotation&lt; Scalar &gt;</h3>

<p>Rotation given by a cosine-sine pair. </p>
<p>This is defined in the Jacobi module.</p><div class="fragment"><div class="line"><span class="preprocessor">#include &lt;Eigen/Jacobi&gt;</span> </div>
</div><!-- fragment --><p>This class represents a Jacobi or Givens rotation. This is a 2D rotation in the plane <code>J</code> of angle \( \theta \) defined by its cosine <code>c</code> and sine <code>s</code> as follow: \( J = \left ( \begin{array}{cc} c &amp; \overline s \\ -s &amp; \overline c \end{array} \right ) \)</p>
<p>You can apply the respective counter-clockwise rotation to a column vector <code>v</code> by applying its adjoint on the left: \( v = J^* v \) that translates to the following <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> code: </p><div class="fragment"><div class="line">v.applyOnTheLeft(J.adjoint());</div>
</div><!-- fragment --><dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a3a08ad41e81d8ad4a37b5d5c7490e765">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a45d91752925d2757fc8058a293b15462">MatrixBase::applyOnTheRight()</a> </dd></dl>
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Public Member Functions</h2></td></tr>
<tr class="memitem:a89c8ea615f8fa77ddd5810a1e5fde4da"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a89c8ea615f8fa77ddd5810a1e5fde4da">adjoint</a> () const</td></tr>
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<tr class="memitem:a38fec2c4da529ef3d05ff37b848b4227"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a38fec2c4da529ef3d05ff37b848b4227">JacobiRotation</a> ()</td></tr>
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<tr class="memitem:a3e8b5dc0a56f7a2d0f788b1ccb1547cb"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a3e8b5dc0a56f7a2d0f788b1ccb1547cb">JacobiRotation</a> (const Scalar &amp;c, const Scalar &amp;s)</td></tr>
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<tr class="memitem:adb5bcb0d28a95e39ca31c2c17e866092"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#adb5bcb0d28a95e39ca31c2c17e866092">makeGivens</a> (const Scalar &amp;p, const Scalar &amp;q, Scalar *r=0)</td></tr>
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<tr class="memitem:a69076401f22e883dc76b6ff9074ac669"><td class="memTemplParams" colspan="2">template&lt;typename Derived &gt; </td></tr>
<tr class="memitem:a69076401f22e883dc76b6ff9074ac669"><td class="memTemplItemLeft" align="right" valign="top">bool&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a69076401f22e883dc76b6ff9074ac669">makeJacobi</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Derived &gt; &amp;, <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> p, <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> q)</td></tr>
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<tr class="memitem:a6572f272cac38e070a99b466dd1fbc74"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#a6572f272cac38e070a99b466dd1fbc74">makeJacobi</a> (const RealScalar &amp;x, const Scalar &amp;y, const RealScalar &amp;z)</td></tr>
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<tr class="memitem:ada8389f291839964d7b481464f0e4e94"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#ada8389f291839964d7b481464f0e4e94">operator*</a> (const <a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> &amp;other)</td></tr>
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<tr class="memitem:ab40e9cdc4582593511e57ee896e055a2"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1JacobiRotation.html#ab40e9cdc4582593511e57ee896e055a2">transpose</a> () const</td></tr>
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<h2 class="groupheader">Constructor &amp; Destructor Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a38fec2c4da529ef3d05ff37b848b4227">&#9670;&nbsp;</a></span>JacobiRotation() <span class="overload">[1/2]</span></h2>

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<p>Default constructor without any initialization. </p>

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<p>Construct a planar rotation from a cosine-sine pair (<em>c</em>, <code>s</code>). </p>

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<h2 class="groupheader">Member Function Documentation</h2>
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<h2 class="memtitle"><span class="permalink"><a href="#a89c8ea615f8fa77ddd5810a1e5fde4da">&#9670;&nbsp;</a></span>adjoint()</h2>

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<p>Returns the adjoint transformation </p>

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<h2 class="memtitle"><span class="permalink"><a href="#adb5bcb0d28a95e39ca31c2c17e866092">&#9670;&nbsp;</a></span>makeGivens()</h2>

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<p>Makes <code>*this</code> as a Givens rotation <code>G</code> such that applying \( G^* \) to the left of the vector \( V = \left ( \begin{array}{c} p \\ q \end{array} \right )\) yields: \( G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )\).</p>
<p>The value of <em>r</em> is returned if <em>r</em> is not null (the default is null). Also note that G is built such that the cosine is always real.</p>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga4cbcafbd33875f185289e750e90d0188">Vector2f</a> v = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Vector2f::Random</a>();</div>
<div class="line">JacobiRotation&lt;float&gt; G;</div>
<div class="line">G.makeGivens(v.x(), v.y());</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the vector v:&quot;</span> &lt;&lt; endl &lt;&lt; v &lt;&lt; endl;</div>
<div class="line">v.applyOnTheLeft(0, 1, G.adjoint());</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the vector J&#39; * v:&quot;</span> &lt;&lt; endl &lt;&lt; v &lt;&lt; endl;</div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_ae814abb451b48ed872819192dc188c19"><div class="ttname"><a href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Eigen::DenseBase::Random</a></div><div class="ttdeci">static const RandomReturnType Random()</div><div class="ttdef"><b>Definition:</b> Random.h:114</div></div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga4cbcafbd33875f185289e750e90d0188"><div class="ttname"><a href="group__matrixtypedefs.html#ga4cbcafbd33875f185289e750e90d0188">Eigen::Vector2f</a></div><div class="ttdeci">Matrix&lt; float, 2, 1 &gt; Vector2f</div><div class="ttdoc">2×1 vector of type float.</div><div class="ttdef"><b>Definition:</b> Matrix.h:500</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is the vector v:
  0.68
-0.211
Here is the vector J' * v:
0.712
    0
</pre><p>This function implements the continuous Givens rotation generation algorithm found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem. LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000.</p>
<dl class="section see"><dt>See also</dt><dd><a class="el" href="classEigen_1_1MatrixBase.html#a3a08ad41e81d8ad4a37b5d5c7490e765">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a45d91752925d2757fc8058a293b15462">MatrixBase::applyOnTheRight()</a> </dd></dl>

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<p>Makes <code>*this</code> as a Jacobi rotation <code>J</code> such that applying <em>J</em> on both the right and left sides of the 2x2 selfadjoint matrix \( B = \left ( \begin{array}{cc} \text{this}_{pp} &amp; \text{this}_{pq} \\ (\text{this}_{pq})^* &amp; \text{this}_{qq} \end{array} \right )\) yields a diagonal matrix \( A = J^* B J \)</p>
<p>Example: </p><div class="fragment"><div class="line"><a class="code" href="group__matrixtypedefs.html#ga36b8989b6aa63020139fc36bae6979e0">Matrix2f</a> m = <a class="code" href="classEigen_1_1DenseBase.html#ae814abb451b48ed872819192dc188c19">Matrix2f::Random</a>();</div>
<div class="line">m = (m + m.adjoint()).eval();</div>
<div class="line">JacobiRotation&lt;float&gt; J;</div>
<div class="line">J.makeJacobi(m, 0, 1);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix m:&quot;</span> &lt;&lt; endl &lt;&lt; m &lt;&lt; endl;</div>
<div class="line">m.applyOnTheLeft(0, 1, J.adjoint());</div>
<div class="line">m.applyOnTheRight(0, 1, J);</div>
<div class="line">cout &lt;&lt; <span class="stringliteral">&quot;Here is the matrix J&#39; * m * J:&quot;</span> &lt;&lt; endl &lt;&lt; m &lt;&lt; endl;</div>
<div class="ttc" id="agroup__matrixtypedefs_html_ga36b8989b6aa63020139fc36bae6979e0"><div class="ttname"><a href="group__matrixtypedefs.html#ga36b8989b6aa63020139fc36bae6979e0">Eigen::Matrix2f</a></div><div class="ttdeci">Matrix&lt; float, 2, 2 &gt; Matrix2f</div><div class="ttdoc">2×2 matrix of type float.</div><div class="ttdef"><b>Definition:</b> Matrix.h:500</div></div>
</div><!-- fragment --><p> Output: </p><pre class="fragment">Here is the matrix m:
 1.36 0.355
0.355  1.19
Here is the matrix J' * m * J:
 1.64     0
    0 0.913
</pre><dl class="section see"><dt>See also</dt><dd>JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), <a class="el" href="classEigen_1_1MatrixBase.html#a3a08ad41e81d8ad4a37b5d5c7490e765">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a45d91752925d2757fc8058a293b15462">MatrixBase::applyOnTheRight()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a6572f272cac38e070a99b466dd1fbc74">&#9670;&nbsp;</a></span>makeJacobi() <span class="overload">[2/2]</span></h2>

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template&lt;typename Scalar &gt; </div>
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<p>Makes <code>*this</code> as a Jacobi rotation <em>J</em> such that applying <em>J</em> on both the right and left sides of the selfadjoint 2x2 matrix \( B = \left ( \begin{array}{cc} x &amp; y \\ \overline y &amp; z \end{array} \right )\) yields a diagonal matrix \( A = J^* B J \)</p>
<dl class="section see"><dt>See also</dt><dd>MatrixBase::makeJacobi(const MatrixBase&lt;Derived&gt;&amp;, Index, Index), <a class="el" href="classEigen_1_1MatrixBase.html#a3a08ad41e81d8ad4a37b5d5c7490e765">MatrixBase::applyOnTheLeft()</a>, <a class="el" href="classEigen_1_1MatrixBase.html#a45d91752925d2757fc8058a293b15462">MatrixBase::applyOnTheRight()</a> </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#ada8389f291839964d7b481464f0e4e94">&#9670;&nbsp;</a></span>operator*()</h2>

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          <td class="memname"><a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a> <a class="el" href="classEigen_1_1JacobiRotation.html">Eigen::JacobiRotation</a>&lt; Scalar &gt;::operator* </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classEigen_1_1JacobiRotation.html">JacobiRotation</a>&lt; Scalar &gt; &amp;&#160;</td>
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<p>Concatenates two planar rotation </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ab40e9cdc4582593511e57ee896e055a2">&#9670;&nbsp;</a></span>transpose()</h2>

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<p>Returns the transposed transformation </p>

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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="Jacobi_8h_source.html">Jacobi.h</a></li>
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